There is a profound, but frequently ignored relationship between logical consequence (formal implication) and material implication. The first repeats the patterns of the latter, but with a wider modal reach. It is argued that this kinship between formal and material implication simply means that they express the same kind of implication, but differ in scope. Formal implication is unrestricted material implication. This apparently innocuous observation has some significant corollaries: (1) conditionals are not connectives, but arguments; (2) the traditional examples of (...) valid argumentative forms are metalogical principles that express the properties of logical consequence; (3) formal logic is not a useful guide to detect valid arguments in the real world; (4) it is incoherent to propose alternatives to the material implication while accepting the classical properties of formal implication; (5) some of the counter-examples to classical argumentative forms and known conditional puzzles are unsound. (shrink)

The material account of indicative conditionals faces a legion of counterexamples that are the bread and butter in any entry about the subject. For this reason, the material account is widely unpopular among conditional experts. I will argue that this consensus was not built on solid foundations, since these counterexamples are contextual fallacies. They ignore a basic tenet of semantics according to which when evaluating arguments for validity we need to maintain the context constant, otherwise any argumentative form can be (...) rendered invalid. If we maintain the context fixed, the counterexamples to the material account are disarmed. Throughout the paper I also consider the ramifications of this defence, make suggestions to prevent contextual fallacies, and anticipate some possible misunderstandings and objections. (shrink)

Russell’s role in the controversy about the paradoxes of material implication is usually presented as a tale of how even the greatest minds can fall prey to basic conceptual confusions. Quine accused him of making a silly mistake in Principia Mathematica. He interpreted “if- then” as a version of “implies” and called it material implication. Quine’s accusation is that this decision involved a use-mention fallacy because the antecedent and consequent of “if-then” are used instead of being mentioned as the premise (...) and the conclusion of an implication relation. It was his opinion that the criticisms and alternatives to the material implication presented by C. I. Lewis and others would never be made in the first place if Russell simply called the Philonian construction “material conditional” instead of “material implication”. Quine’s interpretation of the topic became hugely influential if not universally accepted. This paper will present the following criticisms against this interpretation: (1) the notion of material implication does not involve a use-mention fallacy, since the components of “if-then” are mentioned and not used; (2) Quine’s belief that the components of “if-then” are used was motivated by a conditional-assertion view of conditionals that is widely controversial and faces numerous difficulties; (3) if anything, it was Quine who could be accused of fallacious reasoning: he ignored that in the assertion of a conditional is the whole proposition that is asserted and not its constituents; (4) the Philonian construction remains counter-intuitive even if it is called “material conditional”; (5) the Philonian construction is more plausible when it is interpreted as a material implication. (shrink)

Different logic systems are motivated by attempts to fix the counter-intuitive instances of classical argumentative forms, e.g., strengthening of the antecedent, contraposition and conditional negation. These counter-examples are regarded as evidence that classical logic should be rejected in favour of a new logic system in which these argumentative forms are considered invalid. It is argued that these logical revisions are ad hoc, because those controversial argumentative forms are implied by other argumentative forms we want to keep. It is impossible to (...) remove an argumentative form from a logical system without getting entangled in an intricate logical web, since these revisions imply the removal of other parts of a system we want to maintain. Consequently, these revisions are incoherent and unwarranted. At the very least, the usual approach in the analysis of counter-examples of argumentative forms must be seriously reconsidered. (shrink)

Intensional evidence is any reason to accept a proposition that is not the truth values of the proposition accepted or, if it is a complex proposition, is not the truth values of its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences when her acceptance is based on intensional evidence, while the logical consequences of the proposition presuppose the acceptance of extensional evidence, e.g., she can refuse the logical consequence of a (...) proposition she accepts because she doesn’t know what are the truth-values of its propositional contents. This tension motivates counterexamples to the negation of conditionals, the propositional analysis of conditionals, hypothetical syllogism, contraposition and or-to-if. It is argued that these counterexamples are non-starters because they rely on a mix of intensionally based premises and extensionally based conclusions. Instead, a genuine counterexample to classical argumentative forms should present circumstances where an intuitively true and extensionally based premise leads to an intuitively false conclusion that is also extensionally based. The other point is that evidentiary concerns about intensionally based beliefs should be constrained by the truth conditions of propositions presented by classical logic, which are nothing more than requirements of coherence in distributions of truth value. It is argued that this restriction also dissolves some known puzzles such as conditional stand-offs, the Adams pair, the opt-out property and the burglar’s puzzle. (shrink)

Professor Stevenson's valuable paper [5] calls attention to a number of discrepancies between ‘if’ in English and its usual translation into the horseshoe of material implication. “This is not a reason for distrusting the horseshoe,” he notes, “which is useful so long as it is taken to mean just what it is defined to mean; and it is not a reason for distrusting our English if's, which in spite of their ambiguities are indispensable to our daily discourse”. Accordingly, Stevenson proposes (...) to develop a “richer logic” than the ordinary one, by adding as primitives certain sentential connectives. He speaks throughout in the old terminology of “propositions” rather than in that of the sentences or statements used to express them. Thus he speaks of atomic and molecular propositions, somehow no doubt as real entities in the world, where talk of atomic and molecular sentences would save him from implicit involvement in the notorious difficulties connected with atomic facts. Finally, the inner structure of atomic sentences, and therewith of molecular ones, is never considered. Many molecular sentences contain quantifiers in interesting ways, the clarification of which would seem essential in getting at their structure. Stevenson, however, has no concern with quantifiers, and does not exhibit the quantificational structure of the English sentences considered. (shrink)

Two uses of ‘if are discussed which do not involve conditions. The first is illustrated in the example ‘If he's here, I don't see him’, the second in ‘He's not a dunce, if a trifle stupid’. A third non‐conditional use, cognate with the first is also mentioned: it would be illustrated in the example ‘If he's a Dutchman, I'll eat my hat’. It is argued that recent attempts to formulate a logic of conditionals have distorted our understanding of ‘if, by (...) ignoring these uses, sometimes deliberately. Specifically, as a result, many arguments involving ‘if have been misjudged as invalid, because the expectation has been that ‘if expresses a condition. It is suggested that the traditional analysis of ‘necessary and sufficient conditions’ in terms of ‘if and only if, is partly to blame for these misunderstandings. And the proper understanding of ‘if’ which emerges shows it is quite fully captured in the propositional calculus. (shrink)